Subgroups — C₅₉×#35200 #28447309

Order 15104.

2294 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2851	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2638	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2599	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2499	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2485	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2432	C₂	1	2	yes	maximal
13	C₅₉×#2327	C₂	1	2	yes	maximal, complemented
14	C₅₉×#2326	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#533	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₅₉	C₂²	1	2	yes	—
22	C₂×#124×C₅₉	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
25	C₄×#41×C₅₉	—	2	8	no	—
26	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
34	C₂×#117×C₅₉	C₂²	1	2	yes	—
35	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₅₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₅₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#398	C₂²	1	4	yes	—
40	C₅₉×#397	C₂²	1	8	yes	—
41	C₅₉×#397	C₂²	1	4	yes	—
42	C₅₉×#395	C₂²	1	4	yes	—
43	C₅₉×#394	C₂²	1	8	yes	—
44	C₅₉×#393	C₂²	1	4	yes	—
45	C₅₉×#391	C₂²	1	2	yes	—
46	C₅₉×#391	C₂²	1	2	yes	—
47	C₅₉×#391	C₂²	1	2	yes	—
48	C₅₉×#390	C₂²	1	2	yes	—
49	C₅₉×#389	C₂²	1	4	yes	—
50	C₅₉×#389	C₂²	1	4	yes	—
51	C₅₉×#388	C₂²	1	8	yes	—
52	C₅₉×#387	C₂²	1	8	yes	—
53	C₅₉×#387	C₂²	1	8	yes	—
54	C₅₉×#387	C₂²	1	8	yes	—
55	C₅₉×#385	C₂²	1	8	yes	—
56	C₅₉×#385	C₂²	1	8	yes	—
57	C₅₉×#384	C₂²	1	2	yes	—
58	C₅₉×#383	C₂²	1	2	yes	—
59	C₅₉×#382	C₂²	1	2	yes	—
60	C₅₉×#382	C₂²	1	2	yes	—
61	C₅₉×#381	C₂²	1	2	yes	—
62	C₅₉×#380	C₂²	1	2	yes	—
63	C₅₉×#380	C₂²	1	4	yes	—
64	C₅₉×#380	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
68	C₅₉×#376	C₂²	1	2	yes	—
69	C₂×#41×C₅₉	—	2	4	no	—
70	C₂×#41×C₅₉	—	2	4	no	—
71	C₂×#41×C₅₉	—	2	4	no	—
72	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
73	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₅₉	—	2	8	no	—
84	C₄⋊Q₈×C₅₉	—	2	4	no	—
85	C₄⋊Q₈×C₅₉	—	2	4	no	—
86	#125×C₅₉	—	2	8	no	—
87	#124×C₅₉	—	2	8	no	—
88	C₂²⋊Q₈×C₅₉	—	2	8	no	—
89	C₂²⋊Q₈×C₅₉	—	2	8	no	—
90	C₄×Q₈×C₅₉	—	2	4	no	—
91	C₄×Q₈×C₅₉	—	2	4	no	—
92	C₄×Q₈×C₅₉	—	2	8	no	—
93	C₄×Q₈×C₅₉	—	2	8	no	—
94	C₄×D₄×C₅₉	—	2	8	no	—
95	C₄×D₄×C₅₉	—	2	8	no	—
96	C₄×D₄×C₅₉	—	2	4	no	—
97	C₄×D₄×C₅₉	—	2	4	no	—
98	#117×C₅₉	—	2	4	no	—
99	#117×C₅₉	—	2	8	no	—
100	#117×C₅₉	—	2	8	no	—
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
116	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
122	C₂×C₄²×C₅₉	—	2	8	no	—
123	C₂×C₄²×C₅₉	D₄	1	8	yes	—
124	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
129	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
134	#95×C₅₉	C₂³	1	4	yes	—
135	#95×C₅₉	C₂³	1	4	yes	—
136	#95×C₅₉	C₂³	1	4	yes	—
137	#95×C₅₉	C₂³	1	2	yes	—
138	#95×C₅₉	C₂³	1	2	yes	—
139	#95×C₅₉	C₂³	1	8	yes	—
140	#95×C₅₉	C₂³	1	8	yes	—
141	#95×C₅₉	C₂³	1	8	yes	—
142	#95×C₅₉	C₂³	1	8	yes	—
143	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
144	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
145	#41×C₅₉	—	2	32	no	—
146	C₂×Q₈×C₅₉	—	2	2	no	—
147	C₂×Q₈×C₅₉	—	2	4	no	—
148	C₂×Q₈×C₅₉	—	2	4	no	—
149	C₂×Q₈×C₅₉	—	2	2	no	—
150	C₂×Q₈×C₅₉	—	2	4	no	—
151	C₂×Q₈×C₅₉	—	2	4	no	—
152	C₂×Q₈×C₅₉	—	4	4	no	—
153	C₂×Q₈×C₅₉	#41	1	4	yes	—
154	C₂×D₄×C₅₉	—	2	4	no	—
155	C₂×D₄×C₅₉	—	2	4	no	—
156	C₂×D₄×C₅₉	—	2	2	no	—
157	C₂×D₄×C₅₉	—	2	4	no	—
158	C₂×D₄×C₅₉	—	2	2	no	—
159	C₂×D₄×C₅₉	#41	1	4	yes	—
160	C₂²×C₄×C₅₉	—	2	4	no	—
161	C₂²×C₄×C₅₉	—	2	4	no	—
162	C₂²×C₄×C₅₉	—	2	4	no	—
163	C₂²×C₄×C₅₉	—	2	2	no	—
164	C₂²×C₄×C₅₉	—	2	2	no	—
165	C₂²×C₄×C₅₉	—	2	4	no	—
166	C₂²×C₄×C₅₉	—	2	4	no	—
167	C₂²×C₄×C₅₉	—	2	4	no	—
168	C₂²×C₄×C₅₉	—	2	8	no	—
169	C₂²×C₄×C₅₉	—	4	2	no	—
170	C₂²×C₄×C₅₉	—	4	4	no	—
171	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
187	C₄⋊C₄×C₅₉	—	2	4	no	—
188	C₄⋊C₄×C₅₉	—	2	4	no	—
189	C₄⋊C₄×C₅₉	—	2	2	no	—
190	C₄⋊C₄×C₅₉	—	2	2	no	—
191	C₄⋊C₄×C₅₉	—	2	4	no	—
192	C₄⋊C₄×C₅₉	—	2	4	no	—
193	C₄⋊C₄×C₅₉	—	2	8	no	—
194	C₄⋊C₄×C₅₉	—	2	8	no	—
195	C₄⋊C₄×C₅₉	—	2	4	no	—
196	C₄⋊C₄×C₅₉	—	2	4	no	—
197	C₄⋊C₄×C₅₉	—	2	16	no	—
198	C₄⋊C₄×C₅₉	—	2	4	no	—
199	C₄⋊C₄×C₅₉	—	2	4	no	—
200	C₄⋊C₄×C₅₉	—	4	8	no	—
201	C₂²⋊C₄×C₅₉	—	2	4	no	—
202	C₂²⋊C₄×C₅₉	—	2	8	no	—
203	C₂²⋊C₄×C₅₉	—	2	16	no	—
204	C₂²⋊C₄×C₅₉	—	2	4	no	—
205	C₂²⋊C₄×C₅₉	—	2	4	no	—
206	C₂²⋊C₄×C₅₉	—	4	4	no	—
207	C₂²⋊C₄×C₅₉	—	4	8	no	—
208	C₄²×C₅₉	—	2	4	no	—
209	C₄²×C₅₉	—	2	4	no	—
210	C₄²×C₅₉	—	2	4	no	—
211	C₄²×C₅₉	—	2	8	no	—
212	C₄²×C₅₉	—	2	4	no	—
213	C₄²×C₅₉	—	2	4	no	—
214	C₄²×C₅₉	C₂×D₄	1	4	yes	—
215	C₄²×C₅₉	C₂×D₄	1	4	yes	—
216	C₄²×C₅₉	C₂×D₄	1	4	yes	—
217	C₄²×C₅₉	C₂×D₄	1	4	yes	—
218	C₂³×C₅₉	—	2	2	no	—
219	C₂³×C₅₉	—	2	1	no	—
220	C₂³×C₅₉	—	2	1	no	—
221	C₂³×C₅₉	—	2	2	no	—
222	C₂³×C₅₉	—	2	2	no	—
223	C₂³×C₅₉	—	2	4	no	—
224	C₂³×C₅₉	—	2	2	no	—
225	C₂³×C₅₉	—	2	4	no	—
226	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
227	C₂³×C₅₉	C₂×#41	1	4	yes	—
228	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
229	Q₈×C₅₉	—	2	8	no	—
230	Q₈×C₅₉	—	4	8	no	—
231	Q₈×C₅₉	—	4	8	no	—
232	D₄×C₅₉	—	2	16	no	—
233	D₄×C₅₉	—	2	8	no	—
234	C₂×C₄×C₅₉	—	2	16	no	—
235	C₂×C₄×C₅₉	—	2	2	no	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	1	no	—
238	C₂×C₄×C₅₉	—	2	2	no	—
239	C₂×C₄×C₅₉	—	2	2	no	—
240	C₂×C₄×C₅₉	—	2	2	no	—
241	C₂×C₄×C₅₉	—	2	2	no	—
242	C₂×C₄×C₅₉	—	2	8	no	—
243	C₂×C₄×C₅₉	—	2	8	no	—
244	C₂×C₄×C₅₉	—	2	2	no	—
245	C₂×C₄×C₅₉	—	2	2	no	—
246	C₂×C₄×C₅₉	—	2	4	no	—
247	C₂×C₄×C₅₉	—	2	4	no	—
248	C₂×C₄×C₅₉	—	2	4	no	—
249	C₂×C₄×C₅₉	—	2	4	no	—
250	C₂×C₄×C₅₉	—	2	4	no	—
251	C₂×C₄×C₅₉	—	2	4	no	—
252	C₂×C₄×C₅₉	—	2	4	no	—
253	C₂×C₄×C₅₉	—	2	4	no	—
254	C₂×C₄×C₅₉	—	2	4	no	—
255	C₂×C₄×C₅₉	—	2	4	no	—
256	C₂×C₄×C₅₉	—	2	4	no	—
257	C₂×C₄×C₅₉	—	2	8	no	—
258	C₂×C₄×C₅₉	—	2	4	no	—
259	C₂×C₄×C₅₉	—	4	4	no	—
260	C₂×C₄×C₅₉	—	4	8	no	—
261	C₂×C₄×C₅₉	—	4	8	no	—
262	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
269	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
270	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
271	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
272	#35200	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂²×C₅₉	—	2	2	no	—
274	C₂²×C₅₉	—	2	4	no	—
275	C₂²×C₅₉	—	2	2	no	—
276	C₂²×C₅₉	—	2	2	no	—
277	C₂²×C₅₉	—	2	8	no	—
278	C₂²×C₅₉	—	4	2	no	—
279	C₂²×C₅₉	—	4	2	no	—
280	C₂²×C₅₉	—	4	2	no	—
281	C₂²×C₅₉	—	4	2	no	—
282	C₂²×C₅₉	—	4	4	no	—
283	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
284	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
285	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
286	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
287	C₂²×C₅₉	#585	1	2	yes	—
288	C₄×C₅₉	—	2	2	no	—
289	C₄×C₅₉	—	2	4	no	—
290	C₄×C₅₉	—	2	2	no	—
291	C₄×C₅₉	—	2	2	no	—
292	C₄×C₅₉	—	2	2	no	—
293	C₄×C₅₉	—	4	4	no	—
294	C₄×C₅₉	—	4	2	no	—
295	C₄×C₅₉	—	4	2	no	—
296	C₄×C₅₉	—	4	4	no	—
297	C₄×C₅₉	—	4	4	no	—
298	C₄×C₅₉	—	4	4	no	—
299	C₄×C₅₉	#525	1	4	yes	—
300	C₄×C₅₉	#536	1	4	yes	—
301	C₂×#533	C₂×C₅₉	1	1	yes	characteristic, complemented
302	C₂×C₄×#41	C₂×C₅₉	1	1	yes	characteristic
303	#2851	C₂×C₅₉	1	4	yes	complemented
304	#2638	C₂×C₅₉	1	4	yes	complemented
305	#2599	C₂×C₅₉	1	4	yes	complemented
306	#2567	C₂×C₅₉	1	1	yes	characteristic, complemented
307	#2563	C₂×C₅₉	1	1	yes	characteristic, complemented
308	#2547	C₂×C₅₉	1	1	yes	characteristic, complemented
309	#2546	C₂×C₅₉	1	1	yes	characteristic, complemented
310	#2499	C₂×C₅₉	1	2	yes	complemented
311	#2485	C₂×C₅₉	1	4	yes	complemented
312	#2432	C₂×C₅₉	1	2	yes	—
313	#2327	C₂×C₅₉	1	2	yes	complemented
314	#2326	C₂×C₅₉	1	2	yes	complemented
315	#2283	C₂×C₅₉	1	1	yes	characteristic, complemented
316	C₂×C₅₉	—	4	2	no	—
317	C₂×C₅₉	—	4	4	no	—
318	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
319	C₂×C₅₉	C₂×#536	1	1	yes	characteristic
320	C₂×C₅₉	#3449	1	1	yes	characteristic
321	C₂×C₅₉	#3515	1	2	yes	—
322	C₂×C₅₉	#3518	1	2	yes	—
323	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
324	#533	—	2	8	no	—
325	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
326	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
327	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
328	C₂×#125	C₂²×C₅₉	1	2	yes	—
329	C₂×#124	C₂²×C₅₉	1	2	yes	—
330	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
331	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
332	C₄×#41	—	2	8	no	—
333	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
334	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
335	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
336	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
337	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
340	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
341	C₂×#117	C₂²×C₅₉	1	2	yes	—
342	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
343	C₂×#117	C₂²×C₅₉	1	2	yes	—
344	C₂²×C₄²	C₂²×C₅₉	1	2	yes	—
345	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
346	#398	C₂²×C₅₉	1	4	yes	—
347	#397	C₂²×C₅₉	1	4	yes	—
348	#397	C₂²×C₅₉	1	8	yes	—
349	#395	C₂²×C₅₉	1	4	yes	—
350	#394	C₂²×C₅₉	1	8	yes	—
351	#393	C₂²×C₅₉	1	4	yes	—
352	#391	C₂²×C₅₉	1	2	yes	—
353	#391	C₂²×C₅₉	1	2	yes	—
354	#391	C₂²×C₅₉	1	2	yes	—
355	#390	C₂²×C₅₉	1	2	yes	—
356	#389	C₂²×C₅₉	1	4	yes	—
357	#389	C₂²×C₅₉	1	4	yes	—
358	#388	C₂²×C₅₉	1	8	yes	—
359	#387	C₂²×C₅₉	1	8	yes	—
360	#387	C₂²×C₅₉	1	8	yes	—
361	#387	C₂²×C₅₉	1	8	yes	—
362	#385	C₂²×C₅₉	1	8	yes	—
363	#385	C₂²×C₅₉	1	8	yes	—
364	#384	C₂²×C₅₉	1	2	yes	—
365	#383	C₂²×C₅₉	1	2	yes	—
366	#382	C₂²×C₅₉	1	2	yes	—
367	#382	C₂²×C₅₉	1	2	yes	—
368	#381	C₂²×C₅₉	1	2	yes	—
369	#380	C₂²×C₅₉	1	4	yes	—
370	#380	C₂²×C₅₉	1	4	yes	—
371	#380	C₂²×C₅₉	1	2	yes	—
372	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
374	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
375	#376	C₂²×C₅₉	1	2	yes	—
376	C₅₉	#35200	1	1	yes	characteristic, direct product factor, Sylow
377	C₂×#41	—	2	4	no	—
378	C₂×#41	—	2	4	no	—
379	C₂×#41	—	2	4	no	—
380	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
381	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
383	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
384	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
386	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
387	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
390	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
391	C₄⋊Q₈	—	2	8	no	—
392	C₄⋊Q₈	—	2	4	no	—
393	C₄⋊Q₈	—	2	4	no	—
394	#125	—	2	8	no	—
395	#124	—	2	8	no	—
396	C₂²⋊Q₈	—	2	8	no	—
397	C₂²⋊Q₈	—	2	8	no	—
398	C₄×Q₈	—	2	4	no	—
399	C₄×Q₈	—	2	4	no	—
400	C₄×Q₈	—	2	8	no	—
401	C₄×Q₈	—	2	8	no	—
402	C₄×D₄	—	2	8	no	—
403	C₄×D₄	—	2	8	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	4	no	—
406	#117	—	2	4	no	—
407	#117	—	2	8	no	—
408	#117	—	2	8	no	—
409	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
420	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
430	C₂×C₄²	—	2	8	no	—
431	C₂×C₄²	D₄×C₅₉	1	8	yes	—
432	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
433	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
434	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
435	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
437	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
438	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
442	#95	C₂³×C₅₉	1	4	yes	—
443	#95	C₂³×C₅₉	1	4	yes	—
444	#95	C₂³×C₅₉	1	4	yes	—
445	#95	C₂³×C₅₉	1	2	yes	—
446	#95	C₂³×C₅₉	1	2	yes	—
447	#95	C₂³×C₅₉	1	8	yes	—
448	#95	C₂³×C₅₉	1	8	yes	—
449	#95	C₂³×C₅₉	1	8	yes	—
450	#95	C₂³×C₅₉	1	8	yes	—
451	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
453	#41	—	2	32	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	4	no	—
456	C₂×Q₈	—	2	4	no	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	2	4	no	—
459	C₂×Q₈	—	2	4	no	—
460	C₂×Q₈	—	4	4	no	—
461	C₂×Q₈	#41×C₅₉	1	4	yes	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	#41×C₅₉	1	4	yes	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
480	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
481	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	8	no	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	16	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	4	8	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	2	16	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	4	4	no	—
515	C₂²⋊C₄	—	4	8	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	4	no	—
519	C₄²	—	2	8	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	4	no	—
522	C₄²	C₂×D₄×C₅₉	1	4	yes	—
523	C₄²	C₂×D₄×C₅₉	1	4	yes	—
524	C₄²	C₂×D₄×C₅₉	1	4	yes	—
525	C₄²	C₂×D₄×C₅₉	1	4	yes	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	2	no	—
534	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
535	C₂³	C₂×#41×C₅₉	1	4	yes	—
536	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
537	Q₈	—	2	8	no	—
538	Q₈	—	4	8	no	—
539	Q₈	—	4	8	no	—
540	D₄	—	2	16	no	—
541	D₄	—	2	8	no	—
542	C₂×C₄	—	2	16	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	8	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	8	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
572	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
573	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
574	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
575	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
576	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
577	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
578	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
579	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
591	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
592	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
593	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
594	C₂²	C₅₉×#585	1	2	yes	—
595	C₄	—	2	2	no	—
596	C₄	—	2	4	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	4	4	no	—
601	C₄	—	4	4	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	4	no	—
606	C₄	C₅₉×#525	1	4	yes	—
607	C₄	C₅₉×#536	1	4	yes	—
608	C₂	—	4	4	no	—
609	C₂	—	4	2	no	—
610	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
611	C₂	C₂×C₅₉×#536	1	1	yes	characteristic
612	C₂	C₅₉×#3449	1	1	yes	characteristic
613	C₂	C₅₉×#3515	1	2	yes	—
614	C₂	C₅₉×#3518	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅₉×#533	C₂	semidirect
3. C₅₉×#2851	C₂	semidirect
4. C₅₉×#2638	C₂	semidirect
5. C₅₉×#2599	C₂	semidirect
6. C₅₉×#2567	C₂	semidirect
7. C₅₉×#2563	C₂	semidirect
8. C₅₉×#2547	C₂	semidirect
9. C₅₉×#2546	C₂	semidirect
10. C₅₉×#2499	C₂	semidirect
11. C₅₉×#2485	C₂	semidirect
13. C₅₉×#2327	C₂	semidirect
14. C₅₉×#2326	C₂	semidirect
15. C₅₉×#2283	C₂	semidirect
272. #35200	C₅₉	direct (N × H)
301. C₂×#533	C₂×C₅₉	semidirect
303. #2851	C₂×C₅₉	semidirect
304. #2638	C₂×C₅₉	semidirect
305. #2599	C₂×C₅₉	semidirect
306. #2567	C₂×C₅₉	semidirect
307. #2563	C₂×C₅₉	semidirect
308. #2547	C₂×C₅₉	semidirect
309. #2546	C₂×C₅₉	semidirect
310. #2499	C₂×C₅₉	semidirect
311. #2485	C₂×C₅₉	semidirect
313. #2327	C₂×C₅₉	semidirect
314. #2326	C₂×C₅₉	semidirect
315. #2283	C₂×C₅₉	semidirect
376. C₅₉	#35200	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₉×#533	2
C₂×C₄×#41×C₅₉	2
C₅₉×#2851	2
C₅₉×#2638	2
C₅₉×#2599	2
C₅₉×#2567	2
C₅₉×#2563	2
C₅₉×#2547	2
C₅₉×#2546	2
C₅₉×#2499	2
C₅₉×#2485	2
C₅₉×#2432	2
C₅₉×#2327	2
C₅₉×#2326	2
C₅₉×#2283	2
#35200	59

Subgroups — C59×#35200 #28447309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35200 #28447309